In this article, we discuss the local rigidity of Clifford-Klein forms of homogeneous spaces of 1-connected completely solvable Lie groups. In fact, we introduce a splitting of the local rigidity: vertical rigidity and horizontal rigidity. By using this splitting, we refine some existing results about the local rigidity and introduce a new approach to Baklouti's conjecture about the local rigidity.

2016-07-25math.DG

Non-existence of standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups

We use a computer-aided approach to prove that there are no standard compact Clifford-Klein forms of homogeneous spaces of exceptional Lie groups. This yields further support for Kobayashi's conjecture about possible compact Clifford-Klein forms. On one hand, our approach is based on the algorithms developed in this work which eliminate the majority of possibilities. On the other hand, we complete the proof using the algorithmic methods of classifying semisimple subalgebras in simple real Lie algebras developed by Faccin and de Graaf, as well as by calculating invariants like a-hyperbolic rank…

2019-09-14math.DG

基于等仿射几何中自仿射性的新美学曲线类

The Klein-Lie W-curves as a new class of aesthetic curves based on self-affinity

Faculty of Engineering, Hachinohe Institute of Technology（八千代工业大学工学部）；Institute of Mathematics for Industry, Kyushu University（九州大学产业数学研究所）

本文在等仿射几何中提出一类具有可扩展自仿射性（ESA）的平面曲线，包含二次曲线和对数螺线，作为CAGD中美学曲线的新类别。

2026-08-25math.DG

带电压缩Kaluza-Klein黑洞度规的对称性分析

Symmetry analysis of the charged squashed Kaluza-Klein black hole metric

本文讨论了黎曼空间中荷电压缩Kaluza-Klein黑洞时空的对称性和守恒律。首先，利用Lie点对称性对基本时空度量进行了全面的群分析，然后计算了该时空度量的$n$维最优系统，即$n=1,\ldots,4$.证明了不存在与$n\geq5$的测地线系统相联系的李对称子代数的$n$维最优系统。然后，求出了使拉格朗日量对应的作用积分保持不变的变换的单参数李群的点对称性（即Noether对称性），并利用Noether定理计算了测地线方程组的守恒律.

2014-08-08math.DG

Klein geometries of high order

Using irreducible representations of semi simple Lie algebras, we construct Klein geometries of arbitrarily high order.

2022-11-04math.DGmath.RT

标准紧Clifford-Klein形式问题的一个解

A solution of the problem of standard compact Clifford-Klein forms

本研究在G、H、L为单且绝对单的假设下，解决了单非紧实李群齐性空间标准紧Clifford-Klein形式的分类问题，给出了约化子群在齐性空间上真余紧作用的充要条件。

2025-02-21math.DG

更多相关论文收起更多论文

仿射$Λ$ -建筑、李群的超幂和黎曼对称空间：Margulis猜想的代数证明

Affine $Λ$-buildings, ultrapowers of Lie groups and Riemannian symmetric spaces: an algebraic proof of the Margulis conjecture

本文给出了非阿基米德实封闭的域上的半单李群的仿射$\RR$-建筑物的一般群论构造，以及更一般的仿射$Λ$ -建筑物的群论构造.使用黎曼对称空间的渐近锥面构造Kleiner-Leeb是一个特例。建筑物的明确知识在这里产生的渐近锥面简化了证明马古利斯猜想由于克莱纳-勒布。

2002-10-24math.DGmath.GT

Klein瓶与射影平面的同构

Diffeomorphisms of the Klein Bottle and Projective Plane

我们计算了Klein瓶和射影平面的保体积仿射李群的黎曼曲率张量和截面曲率。特别是，我们调查的部分曲率的符号，并找到一个可能的分歧与定理的Lukatskii。我们对这个定理提出一个修正。

1994-01-14funct-anhep-thmath.DG

Kleininan流形的谱

The spectrum of Kleininan manifolds

我们得到了实秩1的单李群与凸余紧离散子群的商的Plancherel定理及其对Kleinian流形上丛上局部不变微分算子的谱的推论.我们发展了一个几何版本的散射理论。本文是对dg-ga/9609011的更新，从表示论的角度对dg-ga/9609011进行了完全改写。特别是，我们现在能够显示亚纯的爱森斯坦级数的所有参数。

1998-10-26math.DGmath.RT

Lie Algebroid Invariants for Subgeometry

We investigate the infinitesimal invariants of an immersed submanifold $Σ$ of a Klein geometry $M\cong G/H$, and in particular an invariant filtration of Lie algebroids over $Σ$. The invariants are derived from the logarithmic derivative of the immersion of $Σ$ into $M$, a complete invariant introduced in the companion article, 'A characterization of smooth maps into a homogeneous space'. Applications of the Lie algebroid approach to subgeometry include a new interpretation of Cartan's method of moving frames and a novel proof of the fundamental theorem of hypersurfaces in Euclidean, elliptic …

2018-06-18math.DG

李群$SU(2)$和$SO(3)$上的次黎曼距离

Sub-Riemannian distance on Lie groups $SU(2)$ and $SO(3)$

对特殊的左不变次黎曼度量$ρ$和$d$，计算了李群SU（2）和SO（3）中任意元素之间的距离.为了计算第二个度量的距离，我们基本上使用了李群SU（2）到李群SO（3）上的规范两层覆盖满射$Ω$关于度量$ρ$和$d$是次度量和局部等距的事实。证明是基于先前已知的以F为原点的测地线公式。$Ω$的Klein公式，三角函数及其关系，一个实变量函数的常用微积分。但是为了避免可能的错误，需要足够小心地应用这个简单的工具。

2014-11-19math.DG

A variational principle for Kaluza-Klein type theories

For any positive integer $n$ and any Lie group $\mathfrak{G}$, given a definite symmetric bilinear form on $\mathbb{R}^n$ and an $\hbox{Ad}$-invariant scalar product on the Lie algebra of $\mathfrak{G}$, we construct a variational problem on fields defined on an arbitrary oriented $(n+\hbox{dim}\mathfrak{G})$-dimensional manifold $\mathcal{Y}$. We show that, if $\mathfrak{G}$ is compact and simply connected, any global solution of the Euler--Lagrange equations leads, through a spontaneous symmetry breaking, to identify $\mathcal{Y}$ with the total space of a principal bundle over an $n$-dimens…

2019-04-19gr-qchep-thmath-ph

Rough similarity of left-invariant Riemannian metrics on some Lie groups

We consider Lie groups that are either Heintze groups or Sol-type groups, which generalize the three-dimensional Lie group SOL. We prove that all left-invariant Riemannian metrics on each such a Lie group are roughly similar via the identity. This allows us to reformulate in a common framework former results by Le Donne-Xie, Eskin-Fisher-Whyte, Carrasco Piaggio, and recent results of Ferragut and Kleiner-Müller-Xie, on quasiisometries of these solvable groups.

2022-08-12math.DGmath.GRmath.GT

The geometry of generalized Cheeger-Gromoll metrics on the total space of transitive Euclidean Lie algebroids

Natural metrics (Sasaki metric, Cheeger-Gromoll metric, Kaluza-Klein metrics etc.. ) on the tangent bundle of a Riemannian manifold is a central topic in Riemannian geometry. Generalized Cheeger-Gromoll metrics is a family of natural metrics $h_{p,q}$ depending on two parameters with $p\in\mathbb{R}$ and $q\geq0$. This family has been introduced recently and possesses interesting geometric properties. If $p=q=0$ we recover the Sasaki metric and when $p=q=1$ we recover the classical Cheeger-Gromoll metric. A transitive Euclidean Lie algebroid is a transitive Lie algebroid with an Euclidean prod…

2018-08-03math.DG